Which of the following numbers is a factor of 172? ${4,5,9,11,12}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $172$ by each of our answer choices. $172 \div 4 = 43$ $172 \div 5 = 34\text{ R }2$ $172 \div 9 = 19\text{ R }1$ $172 \div 11 = 15\text{ R }7$ $172 \div 12 = 14\text{ R }4$ The only answer choice that divides into $172$ with no remainder is $4$ $ 43$ $4$ $172$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $172$ $172 = 2\times2\times43 4 = 2\times2$ Therefore the only factor of $172$ out of our choices is $4$. We can say that $172$ is divisible by $4$.